\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t45\_tsep\_2 (TMNYyhNX1SosLo8svj8n7u1SqGvm4TM7GHR)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_pre\_topc~X3~X0)){\unicdbdjdcd}((r3\_tsep\_1~X0~X2~X3){\unicdbdjdcd}\\
((r1\_tsep\_1~X2~X1){\unicdcdcdid}((r1\_tsep\_1~X3~X1){\unicdcdcdid}((r3\_tsep\_1~X0~(k2\_tsep\_1~\\
X0~X2~X1)~(k2\_tsep\_1~X0~X3~X1)){\unicdcdcdhd}(r3\_tsep\_1~X0~(k2\_tsep\_1~X0~X1~X2)~\\
(k2\_tsep\_1~X0~X1~X3)))))))))\end{array}
\label{hyp:ehhdadpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_pre\_topc~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_pre\_topc~X3~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_pre\_topc~X4~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_pre\_topc~X5~X1){\unicdbdjdcd}\\
(((u1\_struct\_0~X2=u1\_struct\_0~X4){\unicdcdcdhd}(u1\_struct\_0~X3=u1\_struct\_0~\\
X5)){\unicdbdjdcd}((r3\_tsep\_1~X0~X2~X3){\unicdbdjded}(r3\_tsep\_1~X1~X4~X5))))))))\end{array}
\label{hyp:ehededpfehdhfgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdcdcdhd}((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_tsep\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_pre\_topc~(k2\_tsep\_1~X0~X1~X2)){\unicdcdcdhd}(m1\_pre\_topc~(k2\_tsep\_1~X0~\\
X1~X2)~X0)))\end{array}
\label{hyp:egehpflgcdpfehdhfgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfehdhfgahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_pre\_topc~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_pre\_topc~X3~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_tsep\_1~X2~X1){\unicdcdcdhd}\\
((\preoh r1\_tsep\_1~X3~X1){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_pre\_topc~X4~X1){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m1\_pre\_topc~X5~X1){\unicdcdcdhd}((X4=k2\_tsep\_1~X0~X2~X1){\unicdcdcdhd}((X5=k2\_tsep\_1~X0~\\
X3~X1){\unicdcdcdhd}((r3\_tsep\_1~X0~X2~X3){\unicdcdcdhd}(\preoh r3\_tsep\_1~X1~X4~X5)))))))))))\end{array}$$
\end{theorem}
\end{document}
